Mathematics demo
Quadratic Equation Solver
Explore the roots, discriminant, vertex, axis of symmetry, and graph of ax² + bx + c = 0 through a live spreadsheet calculation model.
SpreadsheetWeb application example
About this quadratic equation application
A quadratic equation describes a parabola and can have two distinct real roots, one repeated real root, or a pair of complex conjugate roots. Adjust the coefficients from −10 to 10 to see those cases update together.
Every result—including the plotted points and downloadable workbook and PDF—is produced by the pinned SpreadsheetWeb model through an authenticated server-side gateway. No API credential or application identifier is sent to the browser.
Live workbook calculator
Shape the equation and watch every result move
Choose integer coefficients from −10 to 10. The solver recalculates automatically—no submit button required.
Calculated results
Solution profile
Waiting for a valid calculation…
- x₁
- —
- x₂
- —
- x₁
- —
- x₂
- —
Download the workbook output
Reading the solution
One discriminant connects the whole picture
The discriminant Δ = b² − 4ac indicates the root type before the roots are evaluated. Positive values produce two real intercepts, zero produces a repeated intercept at the vertex, and negative values produce complex conjugates.
Two distinct real roots and two x-axis crossings.
One repeated real root where the parabola touches the x-axis.
No real crossing and two complex conjugate roots.
The model identifies the equation as linear or degenerate.
Why publish this model?
Turn spreadsheet mathematics into an interactive lesson
- Classroom explorationLet students compare coefficients, roots, and graph shape without editing workbook formulas.
- Training contentEmbed a guided example alongside explanations and learning resources.
- Formula validationExpose trusted spreadsheet logic through a focused, input-safe web interface.
- Shareable resultsGenerate the workbook’s own Excel and PDF outputs from the same coefficients.
Frequently asked questions
About the quadratic solver
Where are the calculations performed?
The browser sends only a, b, and c to this website. Its server-side gateway authenticates with SpreadsheetWeb and calls one pinned application and transaction.
Why are the coefficients limited to −10 through 10?
Those are the published workbook controls and make the graph easy to compare while still demonstrating real, repeated, complex, and linear cases.
Do the downloads use the same results?
Yes. Both actions recalculate the current coefficients through the same workbook and invoke its exact published Excel export definitions.
Are API credentials visible in the page?
No. Credentials, upstream URLs, workspace and application identifiers, transaction numbers, and export IDs remain server-side.